There are 8.7 X 10^3 tiny
insects living in each square
foot of a field and the field
has 6 X 10^2 square feet.
How many insects are living in
the field?

The total selling price before tax is $261.96.

The sales tax paid is $15.72.

The total cost is  $277.68.

The total selling price before tax is the sum of the prices of the WWE 2K21, Starbucks Vanilla Coffee,  new Keurig K550 and the jeans

$49.99 + $13.99 + $179.99 + $17.99 = $261.96.

Sales tax is the amount of money levied when a good or service is purchased. It is a percentage of the price of an item

Sales tax = tax rate x cost

6% x $261.96 = $15.72

The total price paid is the sum of the sales tax and the  total selling price.

$15.72 +  $261.96 = $277.68

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a. fy interacts well with vector addition and scalar multiplication, satisfying the properties of linearity. Therefore, fy is a linear function. b. the 1 x n matrix representation of fv is [ v1, v2, ..., vn ].

(a) To show that fy is linear, we need to demonstrate that it interacts well with vector addition and scalar multiplication. Let's consider two vectors u and w in R^n and a scalar c.

First, let's evaluate fy(u + w):

fy(u + w) = v · (u + w)

Expanding this expression:

fy(u + w) = v · u + v · w

Now, let's evaluate fy(cu):

fy(cu) = v · (cu)

Expanding this expression:

fy(cu) = c(v · u)

We can see that fy(u + w) = fy(u) + fy(w) and fy(cu) = c * fy(u). Thus, fy interacts well with vector addition and scalar multiplication, satisfying the properties of linearity. Therefore, fy is a linear function.

(b) To find the 1 x n matrix representation of fv, we need to express the function fv(x) = v · x in terms of matrix notation. In this case, the matrix representation will have 1 row and n columns.

Let's write v = [v1, v2, ..., vn] as the vector and x = [x1, x2, ..., xn] as the variable vector.

Then, fv(x) = v · x can be represented using matrix notation as follows:

fv(x) = [v1, v2, ..., vn] · [x1, x2, ..., xn]

The dot product of v and x can be computed as the sum of the element-wise multiplication of the corresponding entries:

fv(x) = v1x1 + v2x2 + ... + vnxn

Therefore, the 1 x n matrix representation of fv is:

[ v1, v2, ..., vn ]

The entries of the matrix are simply the elements of the vector v. Each entry in the matrix corresponds to the coefficient of the variable in the linear combination of x that defines fv(x).

In summary, the 1 x n matrix representation of fv is [ v1, v2, ..., vn ].

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The required simplified solution of the given expression is 2x⁶.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
= -2x³(-x³)

Since we know that, -a × - a = a²,
= 2x³⁺³
= 2x⁶

Thus, the required simplified solution of the given expression is 2x⁶.

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Tomatoes are typically weigh less than cucumbers since the mean for tomato is smaller than the mean weight of cucumbers

From the question, we have the following parameters that can be used in our computation:

The attached table of values

From the table, we have

Mean of tomato = 5.5

Mean of cucumbers = 12.75

Tomato has lesser mean than cucumbers

This means that:

Tomatoes are typically weigh less than cucumbers

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Answer:

Tomatoes are typically lighter than cucumbers since the mean weight for tomatoes is less than the mean weight for cucumbers.

What do the MADs indicate about the vegetables' weights?

The weights of tomatoes vary less than the weights of cucumbers since the MAD for tomatoes is less than the MAD for cucumbers.

Step-by-step explanation:

none hope this helps :)

The slope of the arch at these points is for the equation  y=211. 49-20. 6cosh(0. 03291765x) is  4.852 and -4.852

The height function is  given by  y=211.49- 20. 6 cos h(0. 03291765x), the points  given to us are   (-81, 60) and    (81, 60), now differentiating the height  function  with respect to x, we get:

 y'(x)  =0 +20.6(0. 03291765)sinh(0. 03291765x)

         =   0.67810359 sinh(0. 03291765x)

the slope will be, m =-0.67810359 sinh(0. 03291765x),now  putting  the smallest value of x =-81 ,

the slope will be y'(-81)= -0.67810359 sinh(0. 03291765*-81)

                =0.67810359 sinh(-2.666)

                                    = - 0.67810359*  -7.1563 = 4.852

the slope for   y'(81)= 0.67810359 sinh(2.666)

                                   =- 0.67810359*7.15639 =-4.852

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Answer:

42 ft²

Step-by-step explanation:

Rectangle Area: L * W

\(\bf A=(8ft)(6ft)\)

\(\bf 48 \; ft^2\)

\(\bf A= (3ft)(2ft)\)

\(\bf 6\;ft^2\)

\(\bf 48ft^2-6ft^2\)

\(\boxed{\bf 42\; ft^2}\)

Answer:

42

Step-by-step explanation:

6 x 6 is 36. 3 x 2 is 6. 36 + 6 is 42.

a) The Volume of space that is not occupied is; 13.80 in³

b) The length, are and volume have distinct final units.

c) The Volume of the composite shape is the sum of the Volume of Cone, Volume of Cylinder and  Volume of Hemisphere

a) Tennis ball is usually considered to be a sphere. The formula for volume of sphere is;

V = ⁴/₃πr³

where r is radius.

Since diameter = 2.6 inches, then radius; r = 2.6/2 = 1.3 inches

Thus;

Volume of each tennis ball;

V = ⁴/₃π(1.3)³

For the three tennis balls;

V₃ = 3(⁴/₃π(1.3)³)

V₃ = 8.788π

Volume of the cylindrical container = πr²h

h is height = 3(2.6) = 7.8 inches

V_cyl = π(1.3² * 7.8)

V_cyl = 13.182π

Volume of space not occupied = 13.182π - 8.788π

Volume of space not occupied = 13.80 in³

b) For length, the unit will be singular

For Area, the unit will be squared

For Volume, the unit will be cubed

c) There are three objects that make up the composite object namely; Cone, Cylinder, hemisphere. Thus;

Volume of composite shape = Volume of Cone + Volume of Cylinder + Volume of Hemisphere

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Answer:

y = 9x - 5

Step-by-step explanation:

Slope Intercept Form:  y = mx + b

( m = slope and b = y-intercept form )

Answer:

option c.

by Pythagoras theorem.

hypotenuse²=height ²+base²

20²=x²+12²

400=x²+144

400-144=x²

256=x²

256½=x

16=x

Answer:

10

Step-by-step explanation:

48-20=28

28-18=10

that is how I see it at least

Answer: x+42x-2

Step-by-step explanation:

Answer: Part A: 4x    Part B: 4x

Step-by-step explanation: you have to add them

well, let's start like the crab, from the back, what would the amount be after 10 years, with a 10.5% annual rate, compounding annually of course.

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$750\\ r=rate\to 10.5\%\to \frac{10.5}{100}\dotfill &0.105\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases} \\\\\\ A=750\left(1+\frac{0.105}{1}\right)^{1\cdot 10} \implies A=750(1.105)^{10}\implies \boxed{A \approx 2035.56}\)

when will it double?  well, hmmm 750 doubled will be 1500, so

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$1500\\ P=\textit{original amount deposited}\dotfill &\$750\\ r=rate\to 10.5\%\to \frac{10.5}{100}\dotfill &0.105\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years \end{cases}\)

\(1500=750\left(1+\frac{0.105}{1}\right)^{1\cdot t} \implies \cfrac{1500}{750}=(1.105)^t\implies 2=1.105^t \\\\\\ \log(2)=\log(1.105^t)\implies \log(2)=t\log(1.105) \\\\\\ \cfrac{\log(2)}{\log(1.105)}=t\implies 6.94\approx t\qquad \textit{about 6 years and 344 days}\)

Answer:

Area= 97.9 km²

Step-by-step explanation:

Angle at w = 180-119-34

Angle at w = 27°

Side XV= x

x/sin27= 26/sin119

x= sin27(26/sin119)

x= 0.454(26/0.8746)

x= 13.5 km

Side WX = y

y/sin 34= 26/sin119

y= sin34(26/sin119)

y= 0.559(26/0.8746)

y= 16.6 km

S= (16.6+13.5+26)/2

S= 56.1/2

S=28.05

Area = √(28.05(28.05-26)(28.05-13.5)(28.05-16.6))

Area=√(28.05(2.05)(14.55)(11.45))

Area=√(9579.772744)

Area=97.8763

Area= 97.9 km²

The bottom left graph is the line of best fit for the graph in this problem.

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

Hence the graph of the line of best fit should have the smallest possible residual values, meaning that the points on the scatter plot are the closest possible to the line.

For this problem, we have that the bottom left graph has the smaller residuals, hence it shows the line of best fit for the data.

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Answer:

B)Yes, all four conditions in BINS have been met.

Step-by-step explanation:

Yes, all four conditions in BINS have been met.

Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.

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Answer:

Rational numbers can be shown in the form of p/q.

The sum of two rational numbers is always rational.

The sum of two irrational numbers is always irrational.

This question is incomplete or incorrect.

None of the choices is equivalent.

Answer:

1.

1632 can be written as 1632/1. Rational

0.25 can be written as 25/100. Rational

0.0300300030... cannot be written as fraction. Irrational

0 is also irrational

2. Sum of two rational number = rational number

Sum of two irrational number = Rational or irrational number

3. Incomplete

Answer:

30 x 24 = 720

720 / 2 = 360

360 inches squared

Answer:

Step-by-step explanation:

There are 3 blue cubes, 8 ref cubes and 4 yellow cubes, which gives a total of 15 cubes.

Now, if you pick 360 times from the bag, the chances to get a blue cube is 100%, because there's only 15 cubes in total. For trial number 16, you wouldn't have any more cubes.

Therefore, after 360 attempts, there's a 100% probability of picking a blue cube.

The chain should be attached at (3, 4) to balance the triangular piece of the mobile.

To find the coordinates where the chain should be attached to balance the triangular piece of the mobile, we can determine the centroid of the triangle. The centroid is the point of intersection of the medians, which are line segments connecting each vertex of the triangle to the midpoint of the opposite side.

Using the given coordinates: (0, 4), (3, 8), and (6, 0), we find the midpoints of the sides: (1.5, 6), (4.5, 4), and (3, 2). The centroid is the average of these midpoints: (3, 4).

Therefore, the chain should be attached at the coordinates (3, 4) to achieve balance. This point represents the center of mass of the triangular piece, ensuring equal distribution of weight and stability when hung from a chain.

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The perimeter and area of the given composite figure are:

Area = 50 cm²

Perimeter = 42 cm

To find the total surface area of the composite figure, we will find the area of each individual surfaces and then add them together.

Formula for area of a triangle is:

Area = ¹/₂ * base * height

Formula for area of a rectangle is:

Area = Length * Width

Thus:

T.S.A = 2(¹/₂ * 4 * 5) + (10 * 3)

T.S.A = 20 + 30

T.S.A = 50 cm²

The perimeter will be the sum of the entire boundary length. Thus:

Perimeter = 3 + 10 + 10 + 3 + 3 + 3 + 5 + 5

Perimeter = 42 cm

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Lois will sell her tee-shirt for $13.20

The percentage profit = \(\frac{profit}{cost price}\) × 100

Profit = Selling price - cost price

Cost price is the total amount expended in making the tee-shirts

cost price includes cost of buying blank shirt , cost of fabric paint and amount Lois pay herself

cost of buying blank shirt = $1

cost of fabric paint = $1

amount Lois pay herself = \(1\frac{1}{2}\) x $6

\(\frac{3}{2}\) x $6 = $9

Total cost price = $1 + $1 + $9 = $11

0.2 = \(\frac{profit}{11}\)

profit = 11 x 0.2 = $2.2

$2.20 = selling price - $11

selling price = $11 + 2.20 = $13.20

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Answer:

10 dimes and 6 quarters.

Step-by-step explanation:

2.50-25-25=2.00-10 dimes = 1.00-4 0.25=0

so

10 dimes and 6 quarters.

Answer:

10 Dimes and 6 Quarters.

Step-by-step explanation:

Important info:

16 Coins

Total = $2.50

Note:

Dimes = 0.10 Cents

Quarters = 0.25 Cents

Question to answer:

How many of each type of coin does she have?

Solution:

10 Dimes = $1.00

6 Quarters = $1.50

$1.00+$1.50 = $2.50

Therefore 10 Dimes and 6 Quarters = $2.50 and = 16 Coin.

Answer:

0 - 1

Step-by-step explanation:

U can do by simple division method to get the answer

Answer:

Thus, the transformation from ABC to A'B'C' is a reflection over the x-axis.

Choice 1.

Step-by-step explanation:

Reflection over the x-axis

Given a point A(x,y), a reflection over the x-axis maps A to the point A' with coordinates A'(x,-y).

The figure shows triangles ABC and A'B'C'. It can be clearly seen the x-coordinates for each vertex of both triangles is the same and the y-coordinate is the inverse of it counterpart. For example A=(5,3) and A'=(5,-3)

Thus, the transformation from ABC to A'B'C' is a reflection over the x-axis.

Choice 1.

Answer:

F

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

EF² + 12² = 19²

EF² + 144 = 361 ( subtract 144 from both sides )

EF² = 217 ( take the square root of both sides )

EF = \(\sqrt{217}\) → F

The length of EF in the right triangle below is √217.

Option F is the correct answer.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Using the Pythagorean theorem,

DE² = EF² + DF²

19² = 12² + EF²

EF² = 361 - 144

EF = √217

Thus,

The length of EF in the right triangle below is √217.

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From given, a probability of picking two bags and with different marble choices, then the probability of picking a certain marble is the probability of combination of certain marble to the probability of combination of total space.

Twelve of Revie's thirty marbles are red, ten are green, and eight are black. Three of his friends are asked to remove and replace a marble. Red balls have a 12/30. Probability of being chosen, blue balls have a 10/30 chance, and black balls have an 8/30 chance. The sum of each probability is equal to (12/30) x (10/30) x (8/30), which is the probability of selecting three different coloured balls. the methods for selecting three balls of various colours. 3! = 3x2x1 = 6. This is due to the fact that there are three ways to select the first ball—red, green, or black—but only two ways to select the second and just one method to select the last (by the same argument).

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The correct option is B) Not valid. Consider the statement “Since some shoes are sneakers, some non-sneakers are non-shoes.”

We know that all sneakers are shoes, but all shoes are not sneakers.  Hence, some shoes are sneakers. But, this statement does not imply that “some non-sneakers are non-shoes.” This inference cannot be drawn by contraposition. So, it is not valid.Inferences cannot be drawn in contraposition all the time. Contraposition is a type of logical statement that involves reversing and negating the terms of an original proposition. It is a logical relationship between a proposition and its converse. If a proposition is true, the contrapositive is always true.An example of contraposition can be shown as follows:“If a person is a human, then they are mortal.”We can write the contrapositive of this statement as:“If a person is not mortal, then they are not human.”

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Answer: 5/8

Step-by-step explanation: remember the "/" sign just means divide.

3 divided by 5=0.6, and 5 divided by 8=0.625, so 5/8 is larger

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation. Word illustration: The product of 8 and 3 is 11

Here, the formula is 4 x – 5 y = 20.

Finding a value for (x, y) that will satisfy the equation above is the next step.

Hit and Trial is THE ONLY WAY POSSIBLE to accomplish this.

Replace it with x = 0.

The formula changes to 4 (0) - 5y = 20.

or, -5 y = 20 ⇒ y = -20/5 = - 4

So, if x = 0, then y = – 4.

The answer to the given problem is therefore (0,-4)

Let's replace that with y = 0.

The formula then reads: 4 (x) - 5(0) = 20.

or, 4 x = 20 ⇒ x = 20/4 = 5

Thus, if x = 5, y = 0.

Therefore, the above equation will be (5, 0).

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The equation will be 4x-5y=20 will be (5,0).

A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation. Word illustration: The product of 8 and 3 is 11

Here, the formula is 4 x-5 y=20.

Finding a value for (x, y) that will satisfy the equation above is the next step.

Hit and Trial is The only way possible to accomplish this.

Replace it with x=0.

The formula changes to 4(0)-5 y=20.

or, \($-5 y=20 \Rightarrow y=-20 / 5=-4$\)

So, if \($x=0$\), then y=-4.

The answer to the given problem is therefore (0,-4)

Let's replace that with \($\mathrm{y}=0$\).

The formula then reads: 4(x)-5(0)=20.

or, \($4 x=20 \Rightarrow x=20 / 4=5$\)

Thus, if x=5, y=0.

Therefore, the above equation will be (5,0).

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